A280919 Precipices from the successive terraces, descending by the main diagonal of the pyramid described in A245092. Also first differences of A071562.

1, 2, 2, 2, 1, 3, 3, 1, 2, 2, 4, 1, 3, 2, 2, 3, 1, 4, 2, 3, 3, 1, 1, 4, 2, 4, 3, 1, 2, 4, 2, 5, 3, 1, 3, 4, 2, 1, 5, 2, 1, 1, 4, 4, 2, 2, 5, 3, 1, 5, 2, 2, 2, 3, 5, 3, 1, 6, 3, 1, 2, 4, 2, 3, 3, 1, 1, 6, 4, 2, 5, 3, 2, 3, 1, 2, 2, 4, 4, 1, 1, 6, 4, 1, 3, 1, 3

Offset: 1

Author

Omar E. Pol, Jan 10 2017

Keywords

• nonn

Comments

Descending by the main diagonal of the pyramid, A071562 gives the levels where we can find a terrace.

The terraces at the k-th level of the pyramid are also the parts of the symmetric representation of sigma(k).

a(n) is the length of the n-th vertical line segment at the main diagonal of the pyramid.

a(n) is the precipice of A071562(n).

The structure of the stepped pyramid arises after the 90-degree-zig-zag folding of the diagram of the isosceles triangle A237593.

The stepped pyramid is also one of the 3D-quadrants of the stepped pyramid described in A244050.

Equals nonzero terms of A259179. - Omar E. Pol, Apr 17 2018

Links

• Robert Price, Table of n, a(n) for n = 1..13750
• Omar E. Pol, Illustration of the isosceles triangle of A237593 (rows 1..28)
• Omar E. Pol, Perspective view of the pyramid (first 16 levels)

Crossrefs

For more information about the precipices see A276112, A277437, A280223 and A280295.

Cf. A000203, A071562, A196020, A235791, A236104, A237048, A237591, A237593, A237270, A237271, A244050, A245092, A259179, A262626.

Programs

Mathematica

Differences@ Select[Range@ 228, Function[n, Total@ Select[Divisors@ n, Sqrt[n/2] <= # < Sqrt[2 n] &] != 0]] (* Michael De Vlieger, Jan 13 2017, after Robert G. Wilson v at A071562 *)

Formula

a(n) = A280223(A071562(n)).

Extensions

More terms from Michael De Vlieger, Jan 13 2017